Article
The Biodiversity Benefits and Opportunity Costs of
Plantation Forest Management: A Modelling Case
Study of Pinus radiata in New Zealand
Nhung Nghiem 1, * and Hop Tran 2
1
2
*
Department of Public Health, University of Otago, P.O. Box 7343, Wellington 6021, New Zealand
Institute of Agriculture and Environment, Massey University, Private Bag 11 222, Palmerston North 4442,
New Zealand; [email protected]
Correspondence: [email protected]; Tel.: +64-4-918-6183
Academic Editor: Timothy A. Martin
Received: 18 September 2016; Accepted: 21 November 2016; Published: 28 November 2016
Abstract: This study modelled the potential biodiversity benefits and the opportunity costs of a
patch-clear-cutting strategy over a clear-cutting strategy for Pinus radiata in New Zealand. Patch-clear
cutting is a special case of clear cutting involving the removal of all the trees from strips or patches
within a stand, leaving the remainder uncut or clear cutting a series of strips or patches. A forest-level
optimisation model was extended to include uncertainty in timber growth, plant diversity, and
cutting costs. Using a species-area relationship and economies of cutting scale, the net present value
and optimal rotation age under alternative management strategies were calculated. Results suggested
that the optimal rotation ages were similar (24 and 25 years) for the two cutting strategies. Patch-clear
cutting provided higher biodiversity benefits (i.e., 59 vs. 11 understorey plant species) with an
opportunity cost of 27 NZD (18 USD) per extra plant species or 1250 NZD (820 USD) ha−1 . However,
the true benefits of patch-clear cutting would be even greater if other benefits of stand retention
are included. Our research can potentially inform local decision making and inform international
systems of payment for environmental services, such as the REDD+ (Reducing Emissions from
Deforestation and Forest Degradation) program, to conserve biodiversity in developing countries
with plantation forests.
Keywords: cutting; modelling; New Zealand; opportunity cost of biodiversity; optimal forest rotation;
Pinus radiata; species-area relationship
1. Introduction
Forests are among the most important providers of ecosystem services [1]. Forests are home to
more than half of the known terrestrial plant and animal species [2], and deforestation is the major
cause of biodiversity loss [3,4]. Since the global annual rate of natural forest loss is 0.3% [5] and appears
difficult to reverse, plantation forests may sometimes be a “lesser evil” compared to agricultural land
as a means to protect indigenous vegetation remnants [6]. Plantation forests are defined as forests
of predominantly introduced species established through planting and/or seeding, and forests of
native species established through planting and/or seeding and managed intensively [5]. Although
only accounting for 7% of total forest cover world-wide, plantation forests provide approximately
50% of total wood production [5]. Moreover, there is abundant evidence that plantation forests can
provide habitat for a wide range of native forest plants, animals, and fungi. For example, exotic tree
plantations can provide important conservation services to protected areas [7]. There is a range of
48 to 135 indigenous and adventive vascular plant species per stand of Pinus radiata plantations in
New Zealand [3].
Forests 2016, 7, 297; doi:10.3390/f7120297
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Several common cutting methods have been applied in plantation forests around the world,
such as clear cutting, patch-clear cutting, and selection cutting [8]. The dominant cutting strategy for
commercial forests in many countries from temperate, boreal, and tropical forests is clear cutting [8,9].
In New Zealand, clear cutting is widely used in both large-scale commercial and small-block farm
forestry [10]. The main aim is to promote the rapid growth of most species of well-defined age
classes in distinct stands to produce high levels of wood raw materials [8]. Patch-clear cutting is
a special case of clear cutting involving the removal of all the trees from strips or patches within a
stand, leaving the remainder uncut, or clear cutting a series of strips or patches over three or more
entries [8]. Patch-clear cutting has less visual impact than clear cutting, and can mimic some natural
stand disturbance processes. Selection cutting involves cutting a tree or several trees in a small patch
to create an uneven-aged stand [8]. Patch-clear cutting and selection cutting have been used in many
countries to maximise biodiversity and ecosystem service conservation [11–13]. Some case studies
include the patch-clear cutting of trembling aspen (Populus tremuloides) in Canada [14] and the use of
selection cutting in Mediterranean forests [15].
Nevertheless, with such more selective cutting methods there is likely to be a trade-off between
biodiversity conservation and timber production [13,16,17]. In forestry, the trade-off between wood
production and non-timber benefits has been examined to estimate the opportunity cost of enhancing
biodiversity. The opportunity cost is defined as the difference in the net present value (NPV) between
a base case (i.e., only timber production) and multi-use case. For example, Calkin et al. [18] examined
timber harvesting and squirrel population dynamics over a 100-year time horizon. They showed
that the timber NPV increases at the expense of squirrel persistence. Applying a similar approach,
Hurme et al. [19] found that the amount of squirrel habitat can be increased without a severe decrease
in harvestable timber volume. These studies applied a dynamic and spatial analysis to optimise an
ecological-economic system, where ecological objectives are animal species.
From an environmental economic approach, many efforts have been made to value biodiversity
using stated preference approaches. However, these studies usually focus more on natural forests
and wetlands than on plantation forests. The most suitable techniques for valuing biodiversity so
far have been contingent valuation methods (CVMs). A CVM survey contains a hypothetical market
or referendum for respondents to state their willingness to pay for the conservation of a specific
species [20]. To date, the most reliable studies on valuing biodiversity are those valuing high profile
species or elements that are familiar to respondents [21,22]. Additionally, biodiversity valuation using
CVM is influenced by the public’s attitudes toward biodiversity. Species that are recognized by the
respondents as being useful or beneficial to humans are more quickly protected than those perceived as
useless or detrimental [22]. Locals who live around wildlife often have different values to people who
live in the cities. For example, some farmers expressed negative attitudes toward elephant conservation
because of crop damage by elephants [23]. CVM provides useful insights into the values people assign
to wildlife in general, however, its information turns out not to be very useful for policy analysis [24].
This is because simply knowing that people are willing to pay a large amount to protect a species
says nothing about whether one should manage habitat to protect or enhance the species’ numbers.
(See Nghiem [25] for further discussion around this issue).
According to the Convention on Biological Diversity’s 2010 target [26], at least 30% of all
production plantations should be managed in a suitable manner in order to conserve plant diversity.
To help meet this target, the diversity of the associated plant communities in plantation forests is
worth valuing. Our study examined the relationship between timber production and associated plant
diversity in order to estimate the opportunity cost of conserving biodiversity via a patch-clear-cutting
strategy in plantation forests. We used the species–area relationship to predict the dynamics of species
richness in relation to habitat area dynamics. We calculated the opportunity cost of biodiversity from a
private point of view by considering the NPV under clear-cutting and patch-clear-cutting strategies.
In order to calculate the NPV, we extended the forest-level optimisation model by Nghiem [27,28] to
Forests 2016, 7, 297
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include uncertainty in timber growth, plant diversity, and cutting costs. We also performed various
sensitivity analyses of the model to the key model inputs.
Our study shows how this opportunity cost can be estimated along with estimates on the costs of
changing management strategies. This method therefore provides a rapid assessment of biodiversity
value in a plantation forest with a patch-clear-cutting strategy. Unlike the CVM method, our approach
allows one to directly detect the benefits of a non-market service like biodiversity. However, it should
be noted that biodiversity is a non-market good or service, therefore our financial approach may only
express a limited portion of its value. The opportunity cost can be considered as a potential way to
inform the compensation of forest owners who promote biodiversity in their forests. We then applied
this model to a case study of Pinus radiata D. Don in New Zealand.
2. Materials and Methods
2.1. The Model
We extended an earlier forest-level optimisation model by Nghiem [29] to access level of species
richness, and to estimate opportunity costs for different cutting practices. The previous model
considered a plantation forest that consisted of 1 × n stands, but in this study, we improved the
model so that it could include a forest with two dimensions, n × n stands. Let aijt and xijt be the area
and the age of stand i, j (i, j = 1 . . . n) in period t, respectively. In this study, we considered a forest
with one among two alternative forest cutting practices: clear-cutting and patch-clear-cutting. Let dijt
be a control parameter of stand i, j in period t, where dijt = 1 or 0 denotes clear cutting or no action
taken, respectively:
(
0 if dijt = 1
xijt+1 =
(1)
xijt + 1 if dijt = 0
Let qt be the cutting volume of timber in period t, where the timber growth is a function of age
xijt in a form of Gompertz model used by Woollons and Whyte [30] as follows:
xijt
Q( xijt ) = exp( a0 − b0 c0 )
(2)
where the parameter a0 represents a maximum asymptotic yield, b0 and c0 control growth rate while in
trajectory towards a0 at a certain age xijt .
Let bt be a positive discount factor and pt be the price of timber. We assumed pt varied with
timber age t. For simplicity, we assumed that the planting cost, the initial value of forest, and the
value of standing timber at the end time T were constant. Let A be an age at which forest stands
generate a suitable habitat for understorey plant species to survive, hence plant species other than
dominant trees only appear in the forest stands, which reach age A and beyond. Age of forests
was found to explain the species richness variation in plantation forests. Keenan et al. [31] suggest
that this could be induced in their case by the fact that the density of recruited tree seedlings also
increased with plantation age. Older plantation forests established on previously forested lands
are generally expected to support higher levels of diversity given the additional time to develop
structural complexity [32,33]. Additionally, it has been shown that the succession of indigenous and
adventive species in the understorey of plantations is related to temporal changes in the structure of
the canopy [3].
Forest stands can be divided into three age groups: zero (i.e., being cut), equal to or greater than A,
and smaller than A. Spatially connected stands of a same age group, either zero or equal to or greater
than A, form a cluster.
Let ht and lt denote the total area of stands and the number of clusters aged equal to or greater
than A in period t. Then ht = ∑lwt =1 hwt where hwt is the area of stands aged equal to or greater than A
of cluster w in period t.
Forests 2016, 7, 297
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lt
ht =
∑
n
∑ aijt ,
hwt =
w =1
xijt ≥ A
(3)
ij=1
When a forest stand reaches age A, it creates a favourable habitat for a certain type of understorey
plant species (e.g., an indigenous plant species).
Let S be the number of species in a cluster w, and the species richness that relates to the landscape
area is defined by Preston [34] with the power relationship described by:
S (hwt ) = hzwt
(4)
Equation (4) was used by Roy et al. [35] to calculate species richness for each connected available
habitat in each period. They found that z ∈ [0, 0.32] is the value of the exponent for the dynamic
landscape. We used this magnitude of z to calculate species richness for each connected available
habitat at each time period. The species richness dynamic in these connected stands (or in a cluster),
hwt , evolved similar to the model described by Roy et al. [35]. That is, each cluster independently
followed a species area relation law. This is because understorey species supported by different clusters
could be slightly different in species composition. Hence, the total number of species supported by
different clusters in a plantation forest is calculated as follows:
lt
S ( ht ) =
∑
lt
∑
S (hwt ) =
w =1
hzwt , 0 ≤ z ≤ 0.32
(5)
w =1
t
Let yt represent the total area of cut stands in period t. Then yt = ∑m
w=1 ywt , where mt denotes the
number of clusters cut in period t and ywt is the area of cut stands of cluster w in period t.
yt =
∑ mw=t 1 ywt = ∑ ijn =1 aijt dijt ,
dijt = [0, 1]
(6)
It was assumed that a stand was replanted one year after cutting. The cutting cost of each cut
η
cluster, ϕ (ywt ) per unit volume, varied with the size of the cut cluster, ywt , and ϕ (ywt ) = βywt , β > 0
where β is the slope of harvesting cost and η represents the economies of scale, that is the larger the
cutting area, the smaller the harvesting cost per ha.
Since at any time t, some cut stands may form different clusters, the total cutting cost of the forest
in year t is C (yt ), which is defined as follows.
mt
C (yt ) =
∑
ϕ (ywt ) qwt
(7)
xijt dijt , dijt = [0, 1]
(8)
w =1
where qwt is cutting volume of cluster w in period t.
qt =
mt
n
i =1
ij=1
∑ qwt = ∑ Q
Let NPV denote the NPV from selling timber, the objective of the optimal management was to
maximise NPV:
T
MaxNPV = max ∑ bt [ pt qt − C (yt )] ,
(9)
t =0
Subject to:
T
S=
∑ S ( ht )
t =0
(10)
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In Equation (10), S is the number of species that is maintained in the plantation forest over a
T-year period. The optimal timber revenue, rotation age, and number of species were denoted in turn
as NPV*, T*, S*.
Figure 1 presents the model structure with four modules to decide cutting area and volume,
identify
clusters, assess
profitability and species richness, and find an optimal strategy.
Forests 2016, 7, 297 5 of 18 •
•
•
•
Module
1: Involved calculating timber growth and a decision to cut or keep a stand in period t.
 Module 1: Involved calculating timber growth and a decision to cut or keep a stand in period The decisions
to cut a stand vary with alternative management strategies. We let t run from 0 to T,
t. The decisions to cut a stand vary with alternative management strategies. We let t run from and calculated
timber volume based on Equations (1), (2), and (8).
0 to T, and calculated timber volume based on Equations (1), (2), and (8). Module
2: Involved
identifying
clusters
of clear-cutting
area and
habitat
area. area. We ran
through
 Module 2: Involved identifying clusters of clear‐cutting area of
and of habitat We ran stand through 1 to stand
n
×
n,
ascertained
whether
d
=
1
(i.e.,
cut)
or
x
≥
A
(i.e.,
habitat
for
plant
ijt
ijt
stand 1 to stand n × n, ascertained whether 1 (i.e., cut) or (i.e., species),
and
checked
whether
its
adjacent
stands
are
cut
or
aged
older
than
A.
If
satisfied,
clusters
habitat for plant species), and checked whether its adjacent stands are cut or aged older than of clear
cutting or habitat were recorded.
A. If satisfied, clusters of clear cutting or habitat were recorded. Module 3: Involved calculating the NPV using Equations (6)–(9) and counting the number of
 Module 3: Involved calculating the NPV using Equations (6)–(9) and counting the number of species by applying Equations (5) and (10).
species by applying Equations (5) and (10). Module 4: Involved all scenarios with different rotation ages being compared based on the
 Module 4: Involved all scenarios with different rotation ages being compared based on the objective
variable. Then, the scenario that achieved the highest value of the NPV was chosen as
objective variable. Then, the scenario that achieved the highest value of the NPV was chosen the optimal management strategy in terms of timber extraction. The associated NPV and rotation
as the optimal management strategy in terms of timber extraction. The associated NPV and length were referred to as NPV* and T*.
rotation length were referred to as NPV* and T*. Figure 1. Model structure showing four modules to decide “Forest harvest area and volume”, identify Figure
1. Model structure showing four modules to decide “Forest harvest area and volume”, identify
“clusters (connected stands)”, assess “profitability (timber Net Present Value (NPV))” and “species “clusters
(connected stands)”, assess “profitability (timber Net Present Value (NPV))” and “species
richness (S) for plant understorey”, and find an optimal strategy (see the text for details). richness
(S) for plant understorey”, and find an optimal strategy (see the text for details).
We applied this model according to clear‐cutting and patch‐clear‐cutting strategies in order to We applied this model according to clear-cutting and patch-clear-cutting strategies in order to
analyse the trade‐off between the economies of cutting scale and species richness. analyseIn the clear‐cutting strategy, a forest manager seeks to maximise the NPV from selling timber the trade-off between the economies of cutting scale and species richness.
In
the
clear-cutting
strategy,
a forest
manager
to maximise
the NPV
from
selling timber
and
and ignores the impacts of this decision on the seeks
enhancement of plant species richness. To take ignores
the impacts of this decision on the enhancement of plant species richness. To take advantage
advantage of the economies of scale (i.e., the larger the cutting area, the smaller the harvesting cost of the
of scale
(i.e.,cuts the larger
cutting
the smaller
the harvesting
cost includes per ha) the
per economies
ha) the forest manager all the the
stands after area,
T* years. The model of this strategy Equations (1)–(9). A stand is harvested (
forest
manager cuts all the stands after T* years. 1) when it reaches year T* (Module 1). The optimal The model of this strategy includes Equations (1)–(9).
∗
, ∗year
, and T*∗ (Module
. management strategy is denoted by A stand
is harvested (dijt = 1) when it reaches
1). The optimal management strategy
∗
∗
∗
In the patch‐clear‐cutting strategy, the forest manager’s objective is to maximise the NPV from is denoted
by NPVc , Tc , and Sc .
timber production but also to promote biodiversity by applying a small clear‐cut size. In this strategy, In the patch-clear-cutting strategy, the forest manager’s objective is to maximise the NPV from
the manager cuts a stand when it reaches T* years without cutting adjacent stands occurring at the timber production but also to promote biodiversity by applying a small clear-cut size. In this strategy,
same time (see Figure 2a,b). This strategy allows clear‐cutting areas to be as fragmented as possible in order to increase landscape heterogeneity. This would help to promote conservation values through variation in the range of age classes of stands and the spatial juxtaposition of stands of different types and ages [36]. The model of this strategy includes Equations (1)–(10). In Module 1, a Forests 2016, 7, 297
6 of 19
the manager cuts a stand when it reaches T* years without cutting adjacent stands occurring at the
same time (see Figure 2a,b). This strategy allows clear-cutting areas to be as fragmented as possible in
order to increase landscape heterogeneity. This would help to promote conservation values through
variation in the range of age classes of stands and the spatial juxtaposition of stands of different types
Forests 2016, 7, 297 6 of 18 and ages [36]. The model of this strategy includes Equations (1)–(10). In Module 1, a stand can be cut
dijt stand = 1 when
it reaches
year
T* or beyond
and
di−T* and di+and 1jt =
1jt = 0 and d0 ij−
1t = 0 and d0 ij+and 1t = 0.
can be cut 1 when it reaches year or 0beyond and ∗ , T ∗ , and S∗ .
∗
∗
∗
The optimal0 management
strategy
is
denoted
by
NPV
and 0. The optimal management strategy is denoted by , , and . c
c
c
(a) (b)
Figure 2. (a) Patch‐clear‐cutting strategy and (b) Clear‐cutting strategy in the modelling. Each square Figure
2. (a) Patch-clear-cutting strategy and (b) Clear-cutting strategy in the modelling. Each
represents a stand. The shaded squares are stands with standing trees, and white squares are square represents a stand. The shaded squares are stands with standing trees, and white squares
harvested stands. are harvested stands.
The opportunity cost (OC) of increasing biodiversity via using a patch‐clear‐cutting strategy The opportunity cost (OC) of increasing biodiversity via using a patch-clear-cutting strategy (over
(over a clear‐cutting strategy) is defined as the difference in the NPV between the two approaches. a clear-cutting
strategy) is defined as the difference in the NPV between the two approaches. Therefore,
Therefore, it is the amount of money foregone when the patch‐clear‐cutting strategy is applied and a it iscertain level of additional biodiversity is achieved as follows: the amount of money foregone when the patch-clear-cutting strategy is applied and a certain level
of additional biodiversity is achieved as follows:
∗
∗
∗
∗
(11) NPVc∗ − NPVP∗
OC
=
(11)
This model (i.e., Equations (1)–(11)) was used to estimate the opportunity cost of plant diversity S∗P − Sc∗
in New Zealand Pinus radiata plantation forests in the next section. This model (i.e., Equations (1)–(11)) was used to estimate the opportunity cost of plant diversity
2.2. A Case Study of Pinus radiata in New Zealand in New
Zealand Pinus radiata plantation forests in the next section.
New Zealand is one of 25 global biodiversity hotspots [37] and yet plantation forests are common (at 7% and 22% of land surface and of total forest area, respectively [38]). As a result, the New Zealand forestry sector contributes 3.4% to annual GDP [39] and is the third largest export industry in New New Zealand is one of 25 global biodiversity hotspots [37] and yet plantation forests are common
(at Zealand [38]. In 2007, approximately 19.3 million m
7% and 22% of land surface and of total forest area,3 of round wood were harvested, of which, 19.0 respectively [38]). As a result, the New Zealand
3 came from the clear felling of 43,000 hectares of plantation forests [40]. million m
forestry sector contributes 3.4% to annual GDP [39] and is the third largest export industry in
3 of roundpurposes In New Zealand, exotic forests are 19.3
planted for m
production only [41]. However, New Zealand
[38].
In 2007,
approximately
million
wood were
harvested,
of which,
plantation forests are further incentivised because of the potential of such forests to sequester carbon 3
19.0 million m came from the clear felling of 43,000 hectares of plantation forests [40].
emissions from other sectors [42]. Forestry was the first sector to enter New Zealand’s Emission In New Zealand, exotic forests are planted for production purposes only [41]. However, plantation
Trading Scheme (ETS), effective from 1 January 2008. This allows new forest plantations to earn forests are further incentivised because of the potential of such forests to sequester carbon emissions
carbon credits through the Kyoto Protocol. Plantation forests could also be promoted as supplying from other sectors [42]. Forestry was the first sector to enter New Zealand’s Emission Trading Scheme
other ecosystem services, such as the maintenance of clean water, erosion control, and habitat (ETS), effective from 1 January 2008. This allows new forest plantations to earn carbon credits through
provision [43]. Currently, exotic trees are the main crops in New Zealand, of which, 89% is Pinus radiata [40]. Pinus radiata was introduced into New Zealand in the 1840s and grows faster here than in any other country, with the typical rotation length being around 28 years [38]. Since clear cutting is popular and preserving biodiversity is becoming important in New Zealand plantations, this study applies the model described in the previous section to find the 2.2. A Case Study of Pinus radiata in New Zealand
Forests 2016, 7, 297
7 of 19
the Kyoto Protocol. Plantation forests could also be promoted as supplying other ecosystem services,
such as the maintenance of clean water, erosion control, and habitat provision [43]. Currently, exotic
trees are the main crops in New Zealand, of which, 89% is Pinus radiata [40]. Pinus radiata was
introduced into New Zealand in the 1840s and grows faster here than in any other country, with the
typical rotation length being around 28 years [38].
Since clear cutting is popular and preserving biodiversity is becoming important in New Zealand
plantations, this study applies the model described in the previous section to find the opportunity
cost of conserving understorey plants in P. radiata forests. In the baseline scenario, we did not put
any restriction on stand age that creates a favourable habitat for any particular species. However,
in sensitivity analyses, we varied this stand age according to species re-colonisation or habitats for
indigenous plant species.
For the P. radiata growth function, we used age and total standing volume from yield tables for
Central North Island [44] since this area is the major plantation area in New Zealand [45]. The growth
data are detailed in Appendix A.
The harvesting cost was obtained from an established database [46,47] with some adjustments,
as detailed in Appendix B.
c = 42.9y−0.118 , R2 = 0.9
(12)
where c is the clear-cutting cost (expressed in NZD m−3 ) and y is the cutting area or the stand size (ha).
In Equation (12), β = 42.9 > 0 and η = −0.118. The cost function implies a decreasing marginal
cost with the cutting area. Since y ≥ 0, the first derivative c0y < 0, hence (12) is a decreasing function.
Therefore, the larger the cutting size, the less expensive the cutting cost m−3 .
We assumed timber prices varied by tree ages. Since there are no data for the timber prices which
vary with the tree ages, we estimated a weighted timber price using the ratio of pulp and logs at each
tree age calculated from an official yield table [44]. This ratio for each tree age was then used to weigh
pulp prices and log prices to create the timber prices associated with the tree ages. We used an average
pulp price of 51 NZD m−3 and an average log price of 135 NZD m−3 in 2011 [48]. These estimated
timber prices are detailed in Appendix A.
Table 1 shows the parameters used in our baseline model. We chose z = 0.3 in our baseline
scenario since the species–area relationship for native forest remnants in New Zealand was assigned
with z = 0.4 [49]. The quality of plantation forest habitat is lower than that of the native remnants
(i.e., more disturbance), and thus can affect the dispersal of the native species. Moreover, we assumed
a forest size of 400 stands to be sufficient to apply a patch-clear-cutting practice, and that the forest
would exist over a 100-year time horizon, as in the literature [18,19]. We used a maximum rotation age
for P. radiata of 40 years, as similar to the age listed in the yield table [44]. We also ran simulations with
a maximum rotation age of 60 years but the optimal age solution was always less than 40 years, thus
we used 40 years to reduce the computational time in uncertainty analyses. The discount rate of 7%
(in real terms) was used as this is the rate that is mainly used in forest valuations in New Zealand [50].
2.3. Sensitivity and Uncertainty Analyses
We performed a sensitivity analysis of the opportunity cost with five parameters: discount rate (r),
the exponent of species–area curve (z), the exponent of cutting cost (η), the size of forest stands (a), and
stand age that creates favourable habitats (A) (see Table 1). Following Roy et al. [35], we assumed the
number of associated plant species follows a species–area relationship. Based on Ogden et al. [51] and
Brockerhoff et al. [6], we adopted stand age A which creates favourable conditions as being between
one and 20 years. We also performed a sensitivity analysis to the cutting strategy (that is, a sustainable
management scenario) by applying a sustainable cutting restriction so that the number of stands
harvested was the same each year. This ensures a sustainable income from the forest and a sustainable
quantity of timber supplied. It also creates a forest with a mixture of young, mature, and old forest
stands that could be a habitat for a wide range of plant species.
Forests 2016, 7, 297
8 of 19
We assumed timber yield followed a normal distribution with a standard deviation (SD). The SDs
(see Appendix A) were derived from the yield table [52] based on timber volumes over different
management strategies (i.e., production with and without thinning). We assumed timber price followed
a normal distribution with a SD of 20% of the point estimate (see Appendix A). We ran 2000 iterations
in the General Algebraic Modeling System (GAMS 23.6.5) [53]. There is no consensus in the literature
regarding how many iterations are enough to guarantee a model convergence. A number of iterations
as small as a few hundred has been applied in the forestry literature [54,55].
Table 1. Parameters used in the model.
Parameters
Unit
Values
Sensitivity
Analyses
Uncertainty Analyses
Forest harvest size (a)
ha
2
1.5–5
No
Total stand (n)
number
400
No
No
Time horizon (T)
year
100
No
No
Yield (q)
m3
See Appendix A
No
Normal distribution
Exponent of the species area curve (z)
numeric
0.3
0.15–0.32
No
Biodiversity age (A)
year
0
8–20
No
Cost exponent (η)
numeric
−0.118
(see Appendix B)
(−0.5)–(−0.2)
No
Price (p)
NZD
See Appendix A
No
Normal distribution
Discount rate (r)
rate
0.07
0–0.15
No
3. Results
In the baseline scenario, the optimal rotation age in the clear-cutting strategy was 24 years, a year
shorter than that in the patch-clear-cutting strategy (Table 2). It is also four years shorter than the
usual 28-year rotation commonly used in New Zealand (with a range of 25 to 35 years) [56]. Species
richness was substantially enhanced with the patch-clear-cutting strategy vs. the clear-cutting strategy
(59 vs. 11 species, respectively, up to a maximal difference of 72 to 11 species). The clear-cutting
strategy, however, was more financially rewarding than the patch-clear-cutting strategy with a gap
of 1137 NZD·ha−1 (14%) of the total forest. As such, the opportunity cost for obtaining one extra
species of understorey plant in a plantation forest was 24 NZD on average. Figure 3 represents the
trade-off between the number of understorey plant species and the NPV in the clear-cutting and
patch-clear-cutting strategies. It is clear that the trade-offs begin to happen at a much higher species
number (around 20 species) for patch-clear-cutting.
Sensitivity analyses suggested that the NPV and hence the opportunity cost were very sensitive to
discount rates (Table 2). The NPV varied between 255 and 20,519 NZD·ha−1 , and therefore made the
opportunity cost per extra species range from 5 to 429 NZD. The optimal rotation age was also sensitive
to discount rates, and was between 16 and 33 years. However, there was only a slight difference
(one year at most) in the optimal rotation ages between the two cutting strategies. Species richness
was not very sensitive to discount rates as expected.
When cutting size was varied between 1.5 and 5 ha, the optimal rotation age remained the same
for the clear-cutting strategy (24 years) and the patch-clear-cutting strategy (25 years). Species richness
increased significantly, ranging from 31 to 72 species·ha−1 , in the patch-clear-cutting strategy. There
was a trade-off between species richness and the NPV as the NPV reduced from 7490 to 6861 NZD·ha−1
in this strategy. As a result, the difference in the NPV between the two cutting strategies ranged from
666 to 1295 NZD·ha−1 . The opportunity cost, in this case, did not vary in the same direction as the
NPV did with regard to the cutting size. The opportunity cost decreased from 33 to 21 NZD·species−1
as the cutting size decreased from 5 to 1.5 ha. That is, the latter was the optimal stand size for a forestry
manager to adopt in terms of low cost per extra species gained (Figure 4a).
Forests 2016, 7, 297
9 of 19
The opportunity cost was not sensitive to the exponent of the species–area curve. It varied
between 23 and 24 NZD per extra species as the exponent increased from 0.15 to 0.32 (see Appendix C).
The higher the exponent, the larger the number of species in plantation forests (between 53 and
60 species for the patch-clear-cutting strategy). An increase in the exponent of the species–area curve
in this case could be a higher level of stand age heterogeneity or an older growth forest.
The opportunity cost (Figure 4b) increased disproportionately from 24 to 111 NZD per extra
species as the favourable stand age (A) increased from 0 to 20 years. Species richness decreased
significantly with an increase in A, ranging from 12 to 41 species·ha−1 in the patch-clear-cutting
strategy and from 2 to 8 species·ha−1 in the clear-cutting strategy. The opportunity cost increased at a
slower rate as the economies of scale of the harvesting went down (Figure 4c). The optimal rotation
age for the clear-cutting strategy (20 years) was five years shorter than that of the baseline scenario.
In the sustainable management scenario, the optimal rotation age varied between 17 and 35 years
(Figure 4d). It is noted that this is a minimum cutting age, so that it helps to create a forest with a
mixture of young, mature, and old forest stands that could be a habitat for a wide range of plant
species. Putting an age restriction on delaying the harvesting for understorey plant species that prefer
old growth forests
increased
the opportunity cost sharply from 34 to 150 NZD per extra
Forests 2016, 7, 297 9 of 18 species.
In the sustainable management scenario, the optimal rotation age varied between 17 and 35 years Table 2. Optimal rotations (T*), species richness (S*), and net present value (NPV*) from the baseline
(Figure 4d). It is noted that this is a minimum cutting age, so that it helps to create a forest with a model and
sensitivity
analyses
for Pinus radiata plantation
forests
in New Zealand.
mixture of young, mature, and old forest stands that could be a habitat for a wide range of plant Scenarios
species. Putting an age restriction on delaying the harvesting for understorey plant species that prefer old growth forests increased the opportunity cost sharply from 34 to 150 NZD per extra species. Clear-Cutting
OC ($) Per
Patch-Clear-Cutting Strategy (P)
Differences (P–C)
Strategy (C)
Extra Species
Table 2. Optimal rotations (T*), species richness (S*), and net present value (NPV*) from the baseline S*
T*
NPV*
∆NPV*
S*
T*
NPV*
∆S* ∆T*
model and sensitivity analyses for Pinus radiata plantation forests in New Zealand. −1
−1
−1
(Species·ha
Baseline
59
)
(Year)
S* (Species∙ha−1) 60
33
Baseline 59 59
26
Varying the discount rate 58
r = 0 60 19
58
r = 0.03 59 17
r = 0.1 58 r = 0.15 58 T* NPV*
(Year) ($∙ha−1) 136,954
25 7,020 26,894
33 3493
136,954 26 139626,894 19 17 (OC $·ha
)
25
7020
Patch‐Clear‐Cutting Strategy (P) Scenarios Varying the discount rate
r=0
r = 0.03
r = 0.1
r = 0.15
($·ha
3,493 11
Clear‐Cutting 24
8157
Strategy (C) S* T* 1211 12
1212 1212 33
24 26
19
33 16
26 12 19 NPV* 157,473
8157 31,064
4098
157,473 1651
31,064 4098 48
1
Differences (P–C) ∆S* 48
47
48 47
47 46
48 47 Note:
OC is12 the 16 opportunity
cost.
1,396 1651 46 )
OC ($) Per −1137
Extra Species ∆NPV* ∆T* ∆NPV*/∆S* (OC $∙ha−1) 0
−
20,519
1 −1137 24 0 0 0 1 0
0
1
−20,519 −4170 −605 −255 −4170
−605 429 −255 88 ∆NPV*/∆S*
24
429
88
13
5
13 5 Note: OC is the opportunity cost. Patch-clearcutting
9,000
Clear-cutting
8,000
7,000
NPV (NZD ha–1)
6,000
5,000
4,000
3,000
2,000
1,000
0
0
10
20
30
40
50
60
70
Species richness (number ha–1)
Figure 3. Trade‐off between the number of understorey plant species conserved and the NPV for all Figure 3. Trade-off
between the number of understorey plant species conserved and the NPV for all
the scenarios in the clear‐cutting and patch‐clear‐cutting strategies in Pinus radiata plantation forests the scenariosin New Zealand. in the clear-cutting and patch-clear-cutting strategies in Pinus radiata plantation forests in
New Zealand.
Forests
2016, 7, 297
Forests 2016, 7, 297 10 of 19
10 of 18 Figure
4. Sensitivity analyses on the opportunity cost (OC) per extra species between the
Figure 4. Sensitivity analyses on the opportunity cost (OC) per extra species between the patch‐clear‐
patch-clear-cutting
and clear-cutting strategies for Pinus radiata plantation forests in New Zealand with
cutting and clear‐cutting strategies for Pinus radiata plantation forests in New Zealand with regards regards
to stand size (a); stand age (b); economies of scale of the harvesting cost (c); and minimum
to stand size (a); stand age (b); economies of scale of the harvesting cost (c); and minimum harvesting harvesting
age (d). age (d).
Timber price and growth uncertainty analyses for optimal rotation and biodiversity of Timber
price and growth uncertainty analyses for optimal rotation and biodiversity of plantation
plantation forests in New Zealand are presented in Table 3. The mean species richness was 58.6 −1
forests in New
Zealand are presented in Table 3. The mean species
richness was 58.6 species·ha
−1) for the patch‐clear‐cutting strategy, species∙ha−1 (95% confidence interval (CI): 57.2–59.4 species∙ha
−1 ) for the patch-clear-cutting
(95% confidence interval (CI):
57.2–59.4
species
·
ha
strategy, and was
−1) for the clear‐cutting practice. The mean and was 11.7 species∙ha−1 (95% CI: 11.4–11.8 species∙ha
−
1
−
1
11.7 species·ha (95% CI: 11.4–11.8 species·ha ) for the clear-cutting practice. The mean optimal
optimal rotation age for both strategies was about 22 years, with the patch‐clear‐cutting being one rotation
age for
strategies
was
22 years,
the
patch-clear-cutting
being
one
year wider
year wider in both
magnitude (95% CI: about
15–32 years vs. with
15–31 years). The mean NPVs were 10,103 and in magnitude
(95%
CI: 15–32
years vs. 15–31
years).
The mean
NPVs were
10,103
and 11,362
NZD
11,362 NZD for the patch‐clear‐cutting and clear‐cutting, respectively. The opportunity cost was for
thetherefore 27 NZD per extra species (95% CI: 23–31 NZD per extra species). patch-clear-cutting and clear-cutting, respectively. The opportunity cost was therefore 27 NZD per
extra species (95% CI: 23–31 NZD per extra species).
Table 3. Timber price and growth uncertainty analyses for optimal rotation and biodiversity of Pinus Table
3. Timber price and growth uncertainty analyses for optimal rotation and biodiversity of Pinus
radiata plantations in New Zealand. radiata plantations in New Zealand.
Patch‐Clear‐Cutting (P) Scenarios Scenarios
Clear‐Cutting (C) Differences (P − C) Patch-Clear-Cutting
(P)
(C)
Differences (P − C)∆NPV
S* T* NPV* Clear-Cutting
T* NPV* ∆S* ∆T* * (OC S* −1
−1
S*
∆NPV* −1
(Species∙ha
) T* (Year) NPV*
($∙ha ) S*
T*
NPV*
∆S*
∆T*
$∙ha
−
1
−
1
−1 ) ) (Species·ha )
(Year)
($·ha )
(OC $·ha
Mean Mean
Median
Median Lower
95% SI
Lower 95% SI Upper
95% SI
Upper 95% SI 58.5958.59 58.4858.48 57.2557.25 59.4 59.4 22.5
23.0
15.0
32.0
22.5 10,103
10,103 11.68 11.68 22.1
22.0
23.0 9985 9,985 11.67 11.67 15.0
15.0 7875 7,875 11.42 11.42 11.79 11.79 31.0
32.0 13,276
13,276 22.1 11,362 11,362 46.90
11,239 11,239 46.81
22.0 8940 8940 45.83
15.0 14,747 14,747 47.61
31.0 46.90 0.4
1.0
46.81 0.0
45.83 1.0
47.61 0.4 −1258
−1258 1.0 −1257
−1257 0.0 −1066
−1066 1.0 −1471
−1471 Notes: T* is optimal rotations, S* is species richness, and NPV* is net present value.
Notes: T* is optimal rotations, S* is species richness, and NPV* is net present value OC ($) Per Extra OC
($) Per
Species Extra
Species
∆NPV*/∆S
∆NPV*/∆S*
* 27 27
27
27 23
23 31
31 Forests 2016, 7, 297
11 of 19
4. Discussion
In a time of rapid climate change, biodiversity conservation in production plantations has been
called for in order to prevent accelerated loss of biodiversity [26]. This study analysed the benefits to
biodiversity and the opportunity cost of adopting a patch-clear-cutting strategy over a clear-cutting
strategy for managing P. radiata plantation forests. Assuming that forest stands at a certain age can
generate a suitable habitat for plant species, the dynamics of species richness follows a power–law
relation with the habitat area. The ecological-economic model therefore implies the higher the level of
heterogeneity in the distribution of stands with different age classes, the higher the species richness,
and the smaller the NPV.
The results suggest substantial biodiversity benefits from the patch-clear-cutting strategy over
the clear-cutting strategy for understorey plant species (i.e., 59 vs. 11 species·ha−1 ). However, the
opportunity cost was non-trivial at 1260 NZD·ha−1 (822 USD·ha−1 ). This opportunity cost ha−1 was
close to an estimate of environmental values for plantation forests in New Zealand (900 NZD·ha−1 )
using choice modelling [57]. Our finding about the opportunity cost was also in line with the
finding [13,58] that the patch-clear-cutting strategy enhances biodiversity but lowers financial returns.
Yet the difference in optimal rotation ages between the two cutting strategies was small (i.e., about one
year), suggesting that forest managers would not need to delay cutting in order to enhance biodiversity
through the patch-clear-cutting strategy. It is stressed that our estimated opportunity cost may only
represent a limited portion of biodiversity value. In the case that the NPV is negative, forest owners
would abandon the forests, and therefore there is no opportunity cost of biodiversity.
Furthermore, the opportunity cost decreased with a decrease in the patch-clear-cutting size.
That is because when patch-clear-cutting size was reduced, the species richness increased and the
timber revenue decreased, but at a slower rate. Our sensitivity analysis results suggested that the
opportunity cost was very sensitive to the discount rate, an important factor in environment and
ecosystem valuation [59–61]. Thus, there was a large difference in the opportunity cost from using a
social discount rate (a low or even zero discount rate) and a private discount rate (a high discount rate)
(see [61–63] for a discussion of social discount rate). The results also implied that it was very costly to
enhance the value of plant species in mature and old growth forests. The scenario analysis indicated
that there was a trade-off between sustainable management and timber revenue. It is relatively
expensive to create a plantation forest with a mixture of young, mature, and old forest stands, which
support the forest structure diversity (and hence plant species diversity).
The model developed in our study can potentially be applied to other types of forests and in other
parts of the world. However, species–area relation parameters, cost parameters, timber prices, and
growth parameters would need to be adapted. The results of this particular model are probably most
transferable to plantation forests in temperate parts of countries such as Chile and Australia since
P. radiata is also a major exotic tree species grown in these countries [9].
In the last half century, about 60% of all ecosystem services have declined [64]. One reason for this
is that the benefits of ecosystems, such as watershed protection and habitat provision, have not been an
integral part of the formal economic system. Paying for ecosystem services has been applied in some
countries, such as Costa Rica, the United States, and South Africa among others [65–67]. For habitat
provision, such as the one generated by using a patch-clear-cutting strategy in our study, it has been
suggested that funding is via direct payment to achieve the socially optimal level of provision [68].
The opportunity costs reported in our study could, therefore, be considered as means to inform the
appropriate payment level to promote biodiversity in plantation forests. In some cases, however,
national policy makers may also wish to consider carbon sequestration associated with different
forestry practices. At national and local levels, policy makers might also wish to reduce erosion and
flood risk and improve fresh water quality in all plantation forests or particular watersheds. In such
cases, they might wish to pay private foresters even more to change forestry practices (or else buy up
forests for the government or even pass laws that require a certain type of forest management). Indeed,
Forests 2016, 7, 297
12 of 19
some Regional Councils in New Zealand have required certain harvesting strategies to protect against
flood risk [69].
These results could also have an implication for implementing the Reducing Emissions from
Deforestation and Forest Degradation (REDD+) mechanism, which considers the role of conservation,
sustainable management of forests, and enhancement of forest carbon stocks. The REDD+ mechanism
has been suggested both to be an effective tool for climate change mitigation (via carbon sequestration)
and to offer the important co-benefits of biodiversity conservation [70].
In our study, only timber values were considered in the calculation of the opportunity cost, other
values such as carbon sequestration, watershed protection, soil preservation, and water quality benefits,
among others, have been ignored [71,72]. If these values were added, then the patch-clear-cutting
strategy could become optimal from a both financial and biodiversity perspective (compared to the
clear-cutting strategy).
In New Zealand, it has been known that specific management actions can benefit particular
threatened species (e.g., clear-cutting edges provide foraging habitat for New Zealand falcons) [73].
Furthermore, it should be noted that the ability of a species to persist in the landscape depends on its
metapopulation dynamics (i.e., by processes of colonization and extinction) [74]. There is evidence
that the shape of the patches can affect the properties of the stand, such as increasing tree mortality
with wind damage [75].
The composition of understorey species is very dependent on the geographic location of the
forest and on the stage of plantation forest development. For example, new plantings on coastal
sands will likely only have a very few species present, whereas forests on the central volcanic plateau
may have a rich understorey of both exotic and indigenous species. In a recently planted P. radiata
in the Kinleith Forest, Allen et al. [76] found up to 35 vascular plant species, 67% of which were
indigenous. This level of species richness was greater than that for many New Zealand natural
forests [76]. Ogden et al. [51] reported similar results from another Kinleith Forest study. This more
recent study included a 67-year-old P. radiata forest, which had a fern understorey structure similar to
that of native podocarp (Podocarpus spp.) and kauri (Agathis australis) forests.
We have not included the costs of fine-scale silvicultural managements such as site preparation
(movement of wood debris, herbicide use, and soil mounding), pruning, stocking, and crop species
selection (including mixtures). The cost functions involved some simplifying assumptions and ignored
such aspects as: steepness of the forest, distance to the main road, size of trees, and types of cutting
machinery (e.g., cable car or ground-based machines). Timber prices for different tree ages were based
on the ratio of pulp and log prices. We did not take into account the fact that trees at the same age
still produce slightly different log sizes as morphological differentiation between trees is a typical
characteristic of any forest stand. However, the uncertainty arising from these limitations was shown
in the timber price and growth uncertainty analyses.
5. Conclusions
This study shows the benefits to biodiversity, NPV, optimal rotation age, and also the opportunity
cost associated with switching from a ‘business-as-usual’ forestry management system focused upon
maximising timber extraction (clear-cutting) to a more biodiversity-friendly forest management system
(patch clear-cutting). Our research can inform local decision making (e.g., financial compensation to
foresters or laws on cutting strategies by local or national governments in priority areas for conservation
or in flood-prone watersheds), however, such work may also inform international systems of payments
for environmental services (e.g., via the REDD+ mechanism) to conserve biodiversity in developing
countries with plantation forests involving P. radiata or other plantation species.
Forests 2016, 7, 297
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Acknowledgments: The first author sincerely thanks participants of the 17th Annual Conference of the European
Association of Environmental and Resource Economists in the Netherlands for helpful comments in an earlier
draft of this study. She also thanks the School of Economics and Finance, Massey University, Palmerston North,
New Zealand for providing her funding to attend the conference. We thank our colleagues, Nick Wilson,
Anne-Gaelle Ausseil, and George Thomson, for their comments on earlier drafts of this article.
Author Contributions: Nhung Nghiem designed the study and formulated the models. Hop Tran and
Nhung Nghiem ran the model and analysed the results. Nhung Nghiem drafted the paper. All the authors
contributed to the writing of the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Table A1. Mean and standard deviation of timber yield and price to be used in the optimisation model
and uncertainty analyses for Pinus radiata in New Zealand.
Age (Years)
(m3 ·ha−1 )
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
a
Timber Volume
0
0
0
0
2
5
12
24
39
59
82
109
137
168
201
234
268
302
337
371
403
436
469
501
527
558
587
614
640
667
693
719
745
769
793
817
840
863
888
913
Standard Deviation (SD)
0
0
0
0
1
3
7
11
17
23
30
36
43
49
54
60
65
69
74
74
76
81
82
85
88
90
93
95
97
100
101
102
104
104
105
104
103
103
101
100
(m3 ·ha−1 )
Timber Price
(NZD·m−3 )
SD (NZD·m−3 )
77.78
77.78
77.78
77.78
77.78
77.78
77.78
77.78
77.78
77.78
77.78
81.46
83.42
85.70
87.88
89.91
91.26
92.48
93.62
94.14
94.58
94.95
95.17
96.93
99.79
100.36
100.80
101.13
101.59
101.81
102.15
102.21
102.41
102.60
102.91
103.10
103.33
103.45
103.57
103.65
15.56
15.56
15.56
15.56
15.56
15.56
15.56
15.56
15.56
15.56
15.56
16.29
16.68
17.14
17.58
17.98
18.25
18.50
18.72
18.83
18.92
18.99
19.03
19.39
19.96
20.07
20.16
20.23
20.32
20.36
20.43
20.44
20.48
20.52
20.58
20.62
20.67
20.69
20.71
20.73
Notes: a Timber prices in 2011 values; Sources: Authors’ estimates based on data by Ministry for Primary
Industries [44] and Ministry for Primary Industries [48].
Forests 2016, 7, 297
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Appendix B
To estimate the harvesting cost function, we estimated mean tree volume (m3 ) as a function of
average piece size (m3 ) from an established database [46] for Pinus radiata.
v = 1.027p2s − 1.652ps + 1.733, R2 = 0.97
(B1)
where v represents mean tree volume and ps is average piece size.
We obtained a relationship between piece size (m3 ) and clear-cutting cost (NZD·m−3 ) for P. radiata
from [77].
0.277
c = 8.912p−
, R2 = 0.98
(B2)
s
where c is the clear-cutting cost.
From Equations (B1) and (B2), we calculated the clear-cutting cost as a function of tree size
(see Table B1).
c = 8.989v−0.163 , R2 = 0.83
(B3)
Because the relationship between the cutting cost and tree size is the same as that of the cutting
cost and harvest size [78], we adopted Equation (B4) below as a function of cutting costs and cutting
sizes. We also took into account other sources to derive the last two columns in Table B1 as follows.
According to official government estimates [79], the cutting cost is disproportionately high on
cutting sizes smaller than 5 ha, and tends to level out on cutting sizes larger than 10 ha. Other
authors [80–82] confirm that the cutting cost increases significantly with smaller cutting sizes. In our
model, we considered 5 ha to be the typical cutting size and adjusted the cutting cost in Equation (B4)
of 7.2 NZD·m−3 [77] to the typical cutting cost of 26 NZD·m−3 in 2005 [47] for the cutting size of 5 ha.
We also adjusted the cutting costs for other cutting sizes by this ratio (multiplying by 26; then dividing
by 7.2). We chose size 50 ha as the maximum cutting size because 86% forest owners in New Zealand
have less than 40 ha [42]. We then adjusted the above cost values in 2007 to 2011 values using the
Consumer Price Index [83].
Table B1 gives the basic details (the last two columns) that we used to estimate the cost function
to apply in the model:
c = 42.9y−0.118 , R2 = 0.9
(B4)
where c is clear-cutting cost (NZD·m−3 ) and y is the cutting area or the stand size (ha).
In Equation (B4), β = 42.9 > 0 and η = −0.118. The cost function implies a decreasing marginal
cost with the cutting area. Since y ≥ 0, the first derivative c0y < 0, hence (B4) is a decreasing function.
Therefore, the larger the cutting size, the less expensive the cutting cost m−3 . Note that c is the
clear-cutting cost per m−3 , not per total standing volume of a stand, since using different measurement
units of c will lead to different shapes of the cost function. The literature on cutting costs suggested the
negative value of η [77,81,84].
Table B1. Data from Pinus radiata plantations used to estimate the cost function of cutting Pinus radiata
in New Zealand.
a
Piece (log)
Size (m3 )
0.8
1.3
2.0
3.0
4.5
a
a
Plantation
Tree Size (m3 )
Harvesting Cost
for a Piece (log)
(NZD·m−3 )
1.1
1.3
2.5
6.0
15.1
10.0
8.0
7.2
6.6
6.0
b
c
c
Stand Size
(ha)
1.0
2.0
5.0
10.0
30.0
d 50.0
Harvesting Cost Per Stand for a
Particular Stand Size on the Left
Column (NZD·m−3 ) in 2011
40.78
32.65
29.37
26.89
25.42
d 24.51
Obtained from [46,77]. A piece is “the underbark volume of an unprocessed merchantable length (of a log)
arriving at the landing”; b Estimated based on Murphy [46,77]; c Adjusted based on Murphy [42,46,47,77–81];
d This value was smoothed from the data for stand size and harvesting cost per stand.
Forests 2016, 7, 297
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Appendix C
Table C1. Optimal rotations (T*), species richness (S*), and net present value (NPV*) from the baseline
model and sensitivity analyses for Pinus radiata plantation forests in New Zealand.
Patch-Clear-Cutting Strategy (P)
Differences (P − C)
Clear-Cutting Strategy (C)
Scenarios
Baseline
OC ($) Per
Extra Species
S*
(Species·ha−1 )
T*
(Year)
NPV*
($·ha−1 )
S*
T*
NPV*
∆S*
∆T*
∆NPV*
(OC $·ha−1 )
∆NPV*/∆S*
59
25
7020
11
24
8157
48
1
−1137
24
20
34
61
1
1
1
−667
−923
−1295
33
28
21
Varying the stand size (ha)—a variable that can be modified by the foresters and planners
a=5
a=3
a = 1.5
31
44
72
25
25
25
7490
7234
6861
11 b
11 b
11 b
24 b
24 b
24 b
8157 b
8157 b
8157 b
Varying the stand age that is assumed to create a suitable habitat for understorey plants (years)
A=8
A = 16
A = 20
42
22
12
25
25
25
7020
7020
7020
8
4
2
24
24
24
8112
8112
8112
34
18
10
1
1
1
−1093
−1093
−1093
33
62
111
7273
7564
7835
8087
12
12
12
12
20
20
20
20
8913
9682
10,251
10,674
47
47
47
47
5
5
5
5
−1640
−2118
−2417
−2586
35
45
51
55
8157 b
8157 b
8157 b
8157 b
47
48
48
49
−7 c
1
4
11
−1626
−4287
−5507
−7318
34
89
114
150
Varying the exponent of the harvesting cost
η = −0.2
η = −0.3
η = −0.4
η = −0.5
59
59
59
59
25
25
25
25
Sustainable management scenario with varied minimum harvesting ages (years)
T: 0–40
T: 25–40
T: 28–40
T: 35–40
58
59
59
60
17
25
28
35
6531
3870
2649
839
11 b
11 b
11 b
11 b
24 b
24 b
24 b
24 b
b
Results from running the baseline scenario for the clear-cutting strategy; c Since in the patch-clear-cutting
strategy, a stand age that creates a favourable condition for understorey species to survive can start from zero,
it could thus accommodate a large number of species (e.g., 58 species/ha) with a short rotation (e.g., 17 years).
As a result, the difference in rotation ages between this strategy and the baseline clear-cutting strategy was
seven years.
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